A non-detachable connecting system is known from EP 0 343 395. In that system, a connecting socket of a plumbing fixture or a cast metal fitting and a pipe which is inserted into the socket and rests against a stop are pressed together from the outside with an externally applied pressing tool (crimping). In order for this non-detachable connection to be tight, the connecting socket or coupler is provided on its outside, in the region of the end thereof, with an annular bead within which an annular packing ring or seal is arranged. As cast material, there is preferably used a red brass alloy to which 2.3% to 3% nickel is added in order to increase its elongation at rupture. The proposed alloy furthermore has a high lead content of 5% so that the dement can be readily machined. This system has the disadvantage that the composition of the alloy and the size of the dimensions of the connecting socket to be pressed together must be maintained within very narrow limits so that the pressing together or the crimping of the cast part and the pipe can be achieved without cracking. Another disadvantage of the known connecting system is that a damaged or worn fitting cannot be replaced without destroying the connecting system.